First, refer to the general instruction for computer graphics assign- ments, provided separately. If somethings do not meet the general requirements, you will lose corresponding points or the whole scores for this assignment.
1. Objective
In computer graphics, the majority of drawing primitives are trian- gles. The goal of this assignment is to learn how to draw and animate such primitives (here, 2D). Precisely, you need to draw and move 2D colored circles on the screen.
2. Triangular Approximation of Circle
In general, a circle is represented by its center position and radius. To draw the circle, we first need to convert it to a finite set of triangle primitives. A common way of doing this is to approximate the circle by dividing it to a number of equal-size triangles. This process is called the “tessellation” or “subdivision.”
Figure 1 illustrates how to approximate a circle using 8 triangles, resulting in an octagon. For your implementation, use more triangles (e.g., 36 or 72 triangles) to obtain a smoother boundary.
Figure 1: An octagonal approximation of a circle.
Given a center position p0 = (x0,y0) and a radius r, you can
compute the coordinates of each boundary vertex as
p0 +r(cosθ,sinθ),
where θ indicates the angle at the xy-plane. In your shader program, you will need to use 4D coordinates for gl Position; in that case, usevec4(x0 +rcosθ, y0 +rsinθ, 0, 1),where0indicatethe z coordinate. For the moment, do not care about the last component 1 (this will be covered later in the course).
Also, recall that the default viewing volume is provided with [−1, 1] for the x, y, and z axes.
3. Requirements
You may start from “cgbase” project, already distributed on the class web.
• If ESCAPE or ’q’ keys are pressed, the program is terminated. • Initializethewindowsizeto1280×720(10pt).
• Theprogramhasmorethan20solidcircles(Figure2)(10pt).
• Yourcircleshouldbeacircle(notanellipse),evenwhenthe window is being resized (10 pt).
• The circles are initialized with random position, radius, color, and speed (10 pt).
• Thecircles’initialpositionsrequiretoavoidcollision(20pt).
• Thecirclesaremovinginrandomdirections(10pt).
• Whenacirclemeetothercirclesorsidewalls,itsdirectionand speed are randomly changed to avoid overlaps (20 pt).
When you animate circles, it is better to compute the amounts of movements based on the time difference between the current and previous frames rather than simply using a frame counter. This ensures that your application runs at the same speed for different machines. It is also good to test your application in a different (e.g., your friend’s) machine in advance.
Computer Graphics, 2018
Assignment 1: Moving Circles Submission Due: Oct. 14 (Sun.), 23:59, at i-campus
Figure 2: An example screenshot of a single animation frame. 4. Mandatory Requirements
What is listed below is mandatory. So, if anything is missing, you lose 50 pt for each.
5.
•
Instancing should be applied for a static vertex buffer. Your vertex buffer should stay constant at run time, which means positioning and coloring of the circles should be implemented using uniform variables.
(Optional) Elastic Collision
It would be better to apply physics to the collision among the circles rather than to rely solely on the random control over velocities; refer to the following link for the elastic collision:
https://en.wikipedia.org/wiki/Elastic collision
When you apply a physically-based collision to your assignment, you get an extra credit of 20 pt. Please note that in your report.
6.
What to Submit
• Source,project,andexecutablefiles(90pt)
• APDFreportfile:YOURID-YOURNAME-A1.pdf(10pt)
• Compress all the files into a single archive and rename it as
YOURID-YOURNAME-A1.7z.